Investigate checked vector kernel performance for v0.4.3

[acgetchell]

Summary

Investigate whether la-stack can recover more vector-kernel performance in v0.4.3 without weakening the parse-don't-validate invariant model introduced in v0.4.2.

Current State

The v0.4.2 finite-proof changes correctly parse public Matrix and Vector storage into private proof-bearing wrappers before computation. This improved correctness, but benchmarks show some small fixed-size kernels, especially dot product, squared norm, and norm-like operations, remain slower than nalgebra/faer.

The LU regression was mostly recovered by moving non-finite factor checks out of cubic update loops while still validating completed factor storage before factors escape. Vector kernels may have a similar correctness-preserving optimization opportunity: keep public methods checked, but avoid unnecessary duplicate passes or copies once proof-bearing values exist.

Investigation Targets

• Measure dot product, squared norm, infinity norm, solve_from_lu, and lu_solve separately against current nalgebra/faer baselines.
• Identify boundary-check cost versus arithmetic cost for small const-generic dimensions.
• Check whether Vector::dot and Vector::norm2_sq can combine parsing and computation more tightly without exposing invalid internal state.
• Add cold-path hints to vector-kernel overflow exits where that matches the existing Matrix/LU/LDLT error-path style.
• Compare public Vector::dot / Vector::norm2_sq against proof-bearing internal FiniteVector paths so the benchmark separates validation cost from arithmetic cost.
• Check whether matrix infinity-norm and symmetry paths have similar duplicate validation or avoidable pass costs before adding any helper abstraction.
• Preserve private proof-bearing wrappers and crate-private unchecked constructors; do not make non-finite storage observable or silently propagated.
• Consider additive internal-only fast paths over FiniteVector where proof already exists.

Stretch Targets

• Investigate whether det_sign_exact can avoid duplicate fast-filter work between det_direct() and det_errbound() for D <= 4.
• Only pursue determinant fast-filter sharing if Criterion shows it matters; split it into a separate issue if the formula consolidation becomes non-trivial.

Acceptance Criteria

• Public APIs still reject unchecked NaN/∞ storage with LaError::NonFinite metadata.
• Internal helpers trust proof-bearing values instead of reparsing the same object repeatedly.
• Dot product, squared norm, infinity norm, solve_from_lu, and lu_solve are measured separately against current nalgebra/faer baselines.
• Public Vector::dot / Vector::norm2_sq are compared against proof-bearing internal FiniteVector paths so validation cost and arithmetic cost are visible separately.
• Vector-kernel overflow exits use cold-path hints where that matches the existing Matrix/LU/LDLT error-path style.
• Matrix infinity-norm and symmetry paths are checked for duplicate validation or avoidable pass costs; any non-trivial helper abstraction is split out or explicitly justified.
• det_sign_exact fast-filter sharing is either measured and implemented, measured and rejected as not worth it, or split into a separate follow-up if the formula consolidation is non-trivial.
• Any performance improvement is validated with bench-vs-linalg or focused Criterion output.
• Documentation and benchmark tables are updated only after a full benchmark run.

Non-Goals

• Do not roll back parse-don't-validate correctness.
• Do not expose FiniteVector, FiniteMatrix, or other proof wrappers publicly without a separate API design decision.
• Do not trade typed error behavior for benchmark wins.
• Do not add generic_const_exprs-dependent APIs or dimension-specialized trait machinery for v0.4.3.